The cover that saved The Eagles from oblivion. Their second album On The Border was a massive flop and the band considered breaking up. Linda Ronstadt talked them out of it. Their third album was One of these Nights.
From On the Border, Lida Ronstadt's covers Desperado.
Actually Desperado (the album and song), 1973, was their 2nd album, On the Border, 1974, was their third and One of These Nights, 1975 was their 4th. Their eponymous debut, Eagles, came out in 1972 with the huge hit Take it Easy and Peaceful Easy Feeling was also a hit. Desperado was a hit before Linda's cover.
It makes no sense that the song Desperado would not be on the album of the same name. So their 1st two albums did very well. Agreed that On the Border was weaker but they were pretty well established by then.